Questions: Find the midpoint of the segment with the following endpoints. (3,-10) and (-2,-5)

Solution Steps

To find the midpoint of a line segment with given endpoints, use the midpoint formula. The formula is \((x_1 + x_2)/2, (y_1 + y_2)/2\), where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the endpoints.

The endpoints of the segment are given as \( (3, -10) \) and \( (-2, -5) \).

To find the midpoint \( M \) of the segment, we use the midpoint formula: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] Substituting the coordinates of the endpoints: \[ M = \left( \frac{3 + (-2)}{2}, \frac{-10 + (-5)}{2} \right) \]

Calculating the x-coordinate: \[ \frac{3 - 2}{2} = \frac{1}{2} \] Calculating the y-coordinate: \[ \frac{-10 - 5}{2} = \frac{-15}{2} = -7.5 \] Thus, the midpoint is: \[ M = \left( \frac{1}{2}, -7.5 \right) \]

Final Answer